It is common practice in electric arc furnaces, and in other applications of steel and metal working industries, to inject, by means of lances or other types of devices, technological gases and liquid and solid fuels above and inside the bath of melting metal.
The purposes of this injection are manifold and known to anyone operating in this field
One problem which operators in this field particularly complain of is how to achieve a nozzle which will make it possible to obtain the maximum productivity in injection operations at supersonic velocity of a gassy flow of oxygen or other technological gases.
In the dimensioning of the supersonic nozzles of the injection devices, from the fluido-dynamic point of view there are two fundamental parameters to take into account in order to ensure maximum performance:
outlet velocity of the gassy jet; PA1 density of the penetrating jet, defined as the ratio between the momentum and the area of the section penetrated.
From the operating point of view, the optimum solution would suggest mounting the injection device on the walls of the furnace, putting the end, or emission nozzle, far from the bath of metal, in such a way as to preserve it from such damaging elements as the extremely high temperature, the splashes of molten metal, corrosion and impacts with the scrap.
This also allows to reduce the cooling requirements of the head of the device.
This operating constraint contrasts with the technological aspects linked to the fluido-dynamic performance of the gassy jet, since it requires a considerable increase in the outlet velocity of the flow to keep density high as it passes through the layer of slag to the point of entry into the bath of metal.
It is also obvious that the farther the emission point of the injection device is from the zone of impact in the bath of metal, the more risk there is of weakening and dispersing the jet, and therefore of loss of performance and precision in the injection.
At present there are no solutions known to the state of the art wherein the problem of dimensioning the nozzles has been faced in the light of satisfying all these contrasting requirements.
Until now, the dimensioning of devices with nozzles of a constant section has been achieved according to conventional criteria of one-dimension calculation, which limit the outlet velocity of the gassy jet to values of not more than 1 Mach.
Moreover, these dimensioning criteria have the disadvantage that, in order to obtain the desired outlet velocity for a given diameter of the injection device and for a given surface roughness, the length of the device must be increased; consequently, to prevent choking, high stagnation pressures have to be used, which often cannot be obtained in practical applications in steel working plants.
By exploiting the geometry of the nozzles with a convergent/divergent development, it has been possible to obtain higher outlet velocities; however, due to the inaccuracies of present dimensioning criteria, based on empirical data or on simplified analytical methods, the velocity and pressure profiles obtained along the nozzle and in correspondence with the outlet thereof often have a high level of instability and therefore limited performance.
When the emergent gassy jet interacts with the surrounding atmosphere of the furnace, high and irreversible pressure losses therefore occur which impede and prevent high performance and operating efficiency being obtained.
Even when more evolved and sophisticated methods have been proposed for dimensioning the nozzles of the lances, (see for example the document by J. D. Anderson Jr. "Fundamentals of Aerodynamics", McGraw-Hill, 1991), these methods have shown themselves to be applicable for dimensioning only the divergent part of the nozzle.
To obtain a complete dimensioning of the entire convergent/divergent development of the nozzle it is necessary to combine that method with a conventional method.
However, adopting that dimensioning method there is the problem of combining the resolution of a field of subsonic motion of an elliptic type with the solution of a field of supersonic motion of a hyperbolic type.
The transition between these two regions of flow gives a field of motion of a parabolic type which is very susceptible to instability.
The present Applicant, in the light of the shortcomings of the state of the art, and taking into account the technological requirements of preparing injection devices with high performance and high functionality, has developed an algorithm of dimensioning and calculation which allows to design nozzles suitable to satisfy all the operational and technological requirements.
The principle of the invention is based on the concept of optimising the conversion of potential energy into kinetic energy, so that the potential energy varies with respect to the axial coordinate of the nozzle following a law of the type with a hyperbolic tangent.
This invention is therefore achieved in a method of dimensioning and calculation which exploits the algorithm mentioned above and allows to obtain many advantages, overcoming the shortcomings of the state of the art.